golden ratio

This number gets its rather illustrious name from the fact that the Greeks thought that a rectangle with ratio of side lengths equal to ϕ was the most pleasing to the eye, and much of classical Greek architecture is based on this premise. In , an aesthetically pleasing aspect of a rectangle with this ratio, from a mathematical viewpoint, is that if we embed and remove a w×w square in the below diagram, the remaining rectangle also has a width-to-length ratio of ϕ.

Above: The golden rectangle; l/w=ϕ.

ϕ has plenty of interesting mathematical , however. Its value is exactly